Rolling motion of non-axisymmetric cylinders

Document Type

Article

Publication Date

10-2005

Abstract

The “Great Soup Can Race” is frequently used as a challenge for high school science teams participating in Science Olympiads and as an illustration of the application of basic physics principles. Students are given various materials to build a cylindrical can that will win the race to the bottom of a ramp. In general, the lesson is intended to be that the system acquiring less rotational energy will have greater translational energy and will therefore win the race. Accordingly, the underlying assumption is that the smaller the moment of inertia—for a given mass added to the can—the faster the can. Although this conclusion is correct for symmetric systems, it is incorrect in general. A non-axisymmetric distribution of the additional mass changes the initial potential energy and the torque distribution and, under proper conditions, produces the fastest system. Additionally, the motion of nonaxisymmetric cylinders is varied and interesting to view, and the corresponding theory is solvable for the case of rotation without slipping. Thus, this system would make an excellent project for undergraduate students who have had Lagrangian mechanics.

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